Spam Detection using Recurrent Neural Networks
Initially, spam detection relied on simple rule based techniques to sort out spam. However following Paul Graham's famed article 'A Plan for Spam'  the Naive Bayes approach became very popular to the point that it became regarded as the baseline for dealing with spam. 

However following breakthroughs in deep learning, researchers have now turned their focus to neural networks to help them deal with the perenial problem of spam emails. Google recently reported that by introducing NN's to g-mail's spam filters. It took them from 99.5% to over 99.9% accuracy, suggesting that neural networks especially when used in conjunction with Bayesian classification may be effective for enhancing spam filters. You can refer to the link below to read about Google's success story https://www.wired.com/2015/07/google-says-ai-catches-99-9-percent-gmail-spam/

Developing a spam filter using neural networks is basically a classification problem. You need to follow the steps below to develop such a system. (Nikhil B 2016)


Collect a dataset of spam and legitimate email messages. Label these datasets. You can find email and spam datasets here http://csmining.org/index.php/spam-email-datasets-.html
Process these messages with feature extraction and vectorising techniques i.e. tf-idf vectorizer, word2vec, bag-of-words e.t.c. 
Once you have vectorised the dataset succesfully, apply a supervised learning NN algorithm i.e. radial basis network, multi-layer perceptron (MLP) or backpropagation.
Train your labelled data-set on the neural network. Once training is complete you can use cross validation to calculate the precision of your trained model using the test dataset. 


Some of the advantages of using NN's for spam detection over other methods include.


Neural networks have a higher accuracy of identifying spam as demonstrated by google. 
They have a lower false positive rate compared to other methods such as rule based techniques.
Their main disadvantage is that they require specialised computing hardware to deploy.


Some old influential papers published in the field include.  

Machine Learning Techniques in Spam Filtering (2004) http://ats.cs.ut.ee/u/kt/hw/spam/spam.pdf

Detecting Spam Blogs: A Machine Learning Approach (2006) https://www.aaai.org/Papers/AAAI/2006/AAAI06-212.pdf

A review of machine learning approaches to Spam filtering (2009) https://www.sciencedirect.com/science/article/pii/S095741740900181X